1. Open https://github.com/dlab-geo/r-geospatial-workshop
   • Download & unzip the zip file
   • Make a note of the folder in which it is located

2. Start RStudio and open a new script file

3. Install required libraries in RStudio - if you do not have them already

install.packages(
  c("sp","rgdal","tmap","classInt","RColorBrewer",
    "ggplot2","leaflet", "ggmap"), dependencies=TRUE
)

Intro to working with geospatial data in R

• Geospatial data files and formats
• Loading geospatial data in R
• R packages for working with geospatial data
• Coordinate reference systems & map projections
• Mapping geospatial data

Key goal is familiarity, competency takes lots of practice

Who are you?

Why are you here?

Open one of the tutorial files in a web browser

Slides r-geospatial-workshop-pt1.html

Tutorial r-geospatial-workshop-pt1-tutorial.html

Raw Code scripts/r-geospatial-workshop-pt1.R

Make sure you can cut and paste into RStudio # Geographic Data

are data about locations on or near the surface of the Earth.

represent location more specifically with coordinates

46.130479, -117.134167

Coordinates only make sense when associated with a CRS!

Geographic Coordinates: Latitude and Longitude

Define:

• the shape of the Earth

• the origin (0,0 point)

• the relationship between the system and the real world

• the units

Because of variations in these, there are many geographic CRSs!

The World Geodetic System of 1984 is the most widely used geographic coordinate reference system.

WGS84 is the default CRS for most GIS software

Almost all longitude and latitude data are assumed to be WGS84 unless otherwise specified

Historical data much trickier

You can

• dynamically determine spatial metrics like area, length, distance and direction

• spatial relationships like intersects, inside, contains, etc

and

• link data by location, like census data and crime data

Spatial data is a broader term than geographic data.

Methods for working with spatial data are valid for geospatial data

All spatial data are encoded with some type of coordinate reference system

Geospatial data require the CRS to be a model of locations on the Earth

Vector and Raster Data

Points, lines and Polygons

Regular grid of cells (or pixels)

• We won’t be covering Raster data in this workshop*

software that can import, create, store, edit, visualize and analyze geospatial data

• represented as geometric data objects referenced to the surface of the earth via CRSs

• with methods to operate on those representations

We call software for working with geospatial data GIS

Geographic Information System

This term is commonly associated with desktop software applications.

Desktop GIS - ArcGIS, QGIS

Spatial Databases - PostgreSQL/PostGIS

Web-based GIS - ArcGIS Online, CARTO

Software geospatial data support - Tableau

Programming languages with geospatial data support

• R, Python, Javascript

You already use R

Reproducibility

Free & Open Source

Strong support for geospatial data and analysis

Cutting edge

Make sure you have the packages we are going to use installed and loaded

Make sure you have set your working directory to the location of the workshop files

install.packages(
  c("sp","rgdal","tmap","classInt","RColorBrewer",
    "ggplot2","leaflet", "ggmap"), dependencies=TRUE
)

There are many approaches to and packages for working with geospatial data in R.

One approach is to keep it simple and store geospatial data in a data frame.

This approach is most common when

• the data are point data in CSV files and

• you want to map rather than spatially transform or analyze the data

sf_properties_25ksample.csv

San Francisco Open Data Portal https://data.sfgov.org

SF Property Tax Rolls

This data set includes the Office of the Assessor-Recorder’s secured property tax roll spanning from 2007 to 2016.

We are using a subset of these data as a proxy for home values.

sfhomes <- read.csv('data/sf_properties_25ksample.csv', 
                    stringsAsFactors = FALSE)

# Take a look at first 5 rows and a few of the columns
sfhomes[1:5,c("YearBuilt","totvalue","AreaSquareFeet","Neighborhood",
              "NumBedrooms")]

Make sure your working directory is set to the folder where you downloaded the workshop files!

sfhomes <- read.csv('data/sf_properties_25ksample.csv', 
                    stringsAsFactors = FALSE)

# Take a look at first 5 rows and a few of the columns
sfhomes[1:5,c("YearBuilt","totvalue","AreaSquareFeet","Neighborhood",
              "NumBedrooms")]

##   YearBuilt totvalue AreaSquareFeet       Neighborhood NumBedrooms
## 1      1923  1031391           2250 West of Twin Peaks           0
## 2      1909   775300           5830   Presidio Heights           3
## 3      1915  1116772           1350     Inner Richmond           2
## 4      1947   860130           1162    Sunset/Parkside           0
## 5      1981   322749           1463     Outer Richmond           3

class(sfhomes)            # what is the data object type?
dim(sfhomes)              # how many rows and columns
str(sfhomes)              # display the structure of the object
head(sfhomes)             # take a look at the first 10 records
summary(sfhomes)          # explore the range of values
summary(sfhomes$totvalue) # explore the range of values for one column
hist(sfhomes$totvalue)    # histogram for the totvalue column

• What columns contain the geographic data?
• Are these data vector or raster data?
• What type of geometry do the data contain?
  • Points, lines, polygons, grid cells?
• What is the CRS of these data?

Use the R base plot function to create a simple map

plot(sfhomes$lon, sfhomes$lat) # using base plot function

Use the R base plot function to create a simple map

plot(sfhomes$lon, sfhomes$lat) # using base plot function

Most widely used plotting library in R

Not specifically for geospatial data

But can be used to make fabulous maps

Great choice if you already know ggplot2

Load the library

library(ggplot2)

Basic map with ggplot

library(ggplot2)

ggplot() + geom_point(data=sfhomes, aes(lon,lat))

Basic map with ggplot

ggplot() + geom_point(data=sfhomes, aes(lon,lat), size=1)

ggplot() + geom_point(data=sfhomes, aes(lon,lat), size=1) + coord_map()

Allows you to associate a map projection with geographic coord data.

Map Projection: mathematial transformation from curved to flat surface

A Projected CRS applies a map projection to a Geographic CRS

All introduce distortion,

• in shape, area, distance, direction, or combo

• the larger the area the greater the distortion

No one map projection best for all purposes

Selection depends on location, extent and purpose

Mercator is the default map projection used by the get_coord() function.

• You don’t have to specify it!

It’s important to know that you can customize the map projection and parameters if you wish.

But doing this is beyond the scope of this workshop.

Data driven symbology

ggplot() + geom_point(data=sfhomes, aes(lon,lat, col=totvalue)) + 
  coord_map()

What’s happening here?

sfhomes_low2high <- sfhomes[order(sfhomes$totvalue, decreasing = FALSE),]

ggplot() + 
  geom_point(data=sfhomes_low2high, aes(lon,lat, col=totvalue)) + 
  coord_map()

Try it - Does the output map look different from previous one?

The order of the data in the data frame changes the map display!

Map the sfhomes data in decreasing order by totvalue.

sfhomes_high2low <- sfhomes[order(sfhomes$totvalue, decreasing = T),]
ggplot() + geom_point(data=sfhomes_high2low, aes(lon,lat, col=totvalue)) + 
  coord_map()

What does this code do?

sfhomes2010_15 <- subset(sfhomes_low2high, as.numeric(SalesYear) > 2009)

ggplot() +
  geom_point(aes(lon, lat, col=totvalue), data = sfhomes2010_15 )  +
  facet_wrap(~ SalesYear)

Visual spatial analysis!

It allows you to:

• Create basemaps on which you can display your data.

• Use the Google Geocoding API to get coordinates for place names and addresses (i.e. to ‘geocode’)

• and more…

Load the libary

library(ggmap)

## Google's Terms of Service: https://cloud.google.com/maps-platform/terms/.

## Please cite ggmap if you use it! See citation("ggmap") for details.

Some ggmap functionality may require you to register a Google API key

Beginning July 2018 Google requires a credit card on file to access online APIs

The setup of an API key is beyond the scope of this workshop. So, we we’ll only call Google APIs as a demo in this tutorial. This way, at least you can still see what’s available to you.

If you happen to already have a configured Google Maps API key (with Geocoding, Geolocation, and Static Maps APIs all enabled), then you are welcome to try this on your machine by running:

register_google(<YOUR_API_KEY_HERE>)

(If you have problems with ggmap you may need to reinstall the library from github.

• See this StackOverflow discussion)

Otherwise, just watch for the next few steps!

#devtools::install_github("dkahle/ggmap")
library(ggmap)

Let’s check out the get_map function. This will allow us to fetch map tiles to display in our maps.

get_map uses a number of online mapping services including Google, Stamen and OpenStreetMap (OSM)

get_map requires as input a location, expressed as point coordinates.

See ?get_map for details

Let’s fetch a simple map on which we can display our points

Here we are centering the map on San Francisco & using the stamen toner-lite basemap.

#Load my API key from file
#(NOTE: THIS WON'T RUN ON OTHERS' MACHINES!)
filename = '/home/drew/Desktop/gmapi.txt'
register_google(gsub('\n', '', readChar(filename, file.info(filename)$size)))

sf_center_point <- c(lon=-122.445144, lat=37.769335 )

sf_map <- get_map(sf_center_point)  

## Source : https://maps.googleapis.com/maps/api/staticmap?center=37.769335,-122.445144&zoom=10&size=640x640&scale=2&maptype=terrain&language=en-EN&key=xxx

ggmap(sf_map)

Syntax similar to ggplot

But ggmap takes the name of the map object returned by get_map()

# ggplot() +

ggmap(sf_map) + 
  geom_point(data=sfhomes, aes(x=lon, y=lat, col=totvalue))

ggmap(sf_map) +
  geom_point(data=sfhomes, aes(x=lon, y=lat, col=totvalue))

That map is fine but the zoom level isn’t right.

We want to zoom in on the data by setting the map extent.

We can set the map extent by centering the map on our data and increasing the zoom level.

• Note: get_map prints a lot of messages to the screen!

# Get the center point of the data
sf_ctr <- c(lon = mean(sfhomes$lon), lat = mean(sfhomes$lat))
sf_ctr  # take a look
 
# create the map - setting the zoom level to 12
sf_basemap <- get_map(sf_ctr, source="stamen", maptype="toner-lite", zoom=12)

## Source : https://maps.googleapis.com/maps/api/staticmap?center=37.758403,-122.439444&zoom=12&size=640x640&scale=2&maptype=terrain&key=xxx

## Source : http://tile.stamen.com/toner-lite/12/653/1582.png

## Source : http://tile.stamen.com/toner-lite/12/654/1582.png

## Source : http://tile.stamen.com/toner-lite/12/655/1582.png

## Source : http://tile.stamen.com/toner-lite/12/656/1582.png

## Source : http://tile.stamen.com/toner-lite/12/653/1583.png

## Source : http://tile.stamen.com/toner-lite/12/654/1583.png

## Source : http://tile.stamen.com/toner-lite/12/655/1583.png

## Source : http://tile.stamen.com/toner-lite/12/656/1583.png

## Source : http://tile.stamen.com/toner-lite/12/653/1584.png

## Source : http://tile.stamen.com/toner-lite/12/654/1584.png

## Source : http://tile.stamen.com/toner-lite/12/655/1584.png

## Source : http://tile.stamen.com/toner-lite/12/656/1584.png

Now, view the data on top of the sf_basemap with ggmap

ggmap(sf_basemap) +
   geom_point(data=sfhomes, aes(x=lon, y=lat, col=totvalue))

Finally, let’s add another geospatial data layer to our ggmap.

You can use this method to add as many layers as you want to a ggmap or ggplot.

Use the read.csv function to read in a file of Bart Station locations. What is the name of the column with the longitude values? latitude?

bart <- read.csv("./data/bart.csv")

# take a look
head (bart)

##           X        Y             STATION OPERATOR DIST  CO
## 1 -122.2833 37.87406      NORTH BERKELEY     BART    4 ALA
## 2 -122.2682 37.86969   DOWNTOWN BERKELEY     BART    4 ALA
## 3 -122.2701 37.85321               ASHBY     BART    4 ALA
## 4 -122.2518 37.84451           ROCKRIDGE     BART    4 ALA
## 5 -122.2671 37.82871           MACARTHUR     BART    4 ALA
## 6 -122.2684 37.80808 19TH STREET/OAKLAND     BART    4 ALA

For the maps from here on out, to deal with a smaller example dataset, we’re going to also subset our data for only those rows that pertain to year 2015.

sfhomes15 <- subset(sfhomes, as.numeric(SalesYear) == 2015)

sfmap_with_bart <- ggmap(sf_basemap) +
  geom_point(data=sfhomes15, aes(x=lon, y=lat))  +
  geom_point(data=bart, aes(x=X,y=Y), col="red", size=3) 

sfmap_with_bart

## Warning: Removed 34 rows containing missing values (geom_point).

SF Landmarks

data/landmarks.csv

landmarks <- read.csv("./data/landmarks.csv")
head(landmarks)

##           X       Y id             name
## 1 -13626151 4551548  1       Coit Tower
## 2 -13630804 4544523  2       Twin Peaks
## 3 -13627654 4548289  3        City Hall
## 4 -13635101 4546904  4 Golden Gate Park

Let’s create a map of the SF homes, BART Stations and Landmarks all together.

sfmap_bart_landmarks <- ggplot() +
  geom_point(data=sfhomes15, aes(x=lon, y=lat))  +
  geom_point(data=bart, aes(x=X,y=Y), col="red", size=3) +
  geom_point(data=landmarks, aes(x=X,y=Y), shape=22, 
             col="black", fill="grey", size=4)

All good - are all layers displayed? If not, why not?

There are limits to what you can do with geospatial data stored in a data frame.

The Landmark data do not have geographic coordinates - longitude and latitude.

You can’t map these with ggmap.

##           X       Y id             name
## 1 -13626151 4551548  1       Coit Tower
## 2 -13630804 4544523  2       Twin Peaks
## 3 -13627654 4548289  3        City Hall
## 4 -13635101 4546904  4 Golden Gate Park

The ESRI Shapefile is the most common file format for geospatial data.

ggplot and ggmap cannot directly read in or plot shapefile data.

• though you can do it with a round-about set of commands :(

ggplot & ggmap can’t answer questions like

• What properties are in the Noe Valley neighborhood?

• What is the average property value in each SF neighborhood?

• What is the area of each SF Neighborhood and the property density?

• What properties are within walking distance (.25 miles) of the Mission neighborhood?

You need spatial data objects and spatial methods for that!

Classes and Methods for Spatial Data

The SP package is most commonly used to construct and manipulate spatial data objects in R.

Hundreds of other R packages that do things with spatial data typically build on SP objects.

library(sp)

Take a look at the different types of spatial object classes supported by sp

getClass("Spatial") 

## Class "Spatial" [package "sp"]
## 
## Slots:
##                               
## Name:         bbox proj4string
## Class:      matrix         CRS
## 
## Known Subclasses: 
## Class "SpatialPoints", directly
## Class "SpatialMultiPoints", directly
## Class "SpatialGrid", directly
## Class "SpatialLines", directly
## Class "SpatialPolygons", directly
## Class "SpatialPointsDataFrame", by class "SpatialPoints", distance 2
## Class "SpatialPixels", by class "SpatialPoints", distance 2
## Class "SpatialMultiPointsDataFrame", by class "SpatialMultiPoints", distance 2
## Class "SpatialGridDataFrame", by class "SpatialGrid", distance 2
## Class "SpatialLinesDataFrame", by class "SpatialLines", distance 2
## Class "SpatialPixelsDataFrame", by class "SpatialPoints", distance 3
## Class "SpatialPolygonsDataFrame", by class "SpatialPolygons", distance 2

We use the S*DF objects most frequently!

• SpatialPointsDataFrame, SpatialLinesDataFrame, SpatialPolygonsDataFrame

Let’s transform the sfhomes15 data frame to an sp object of type SpatialPointsDataFrame

Use the sp::coordinates() method

• Sets or retrieves spatial coordinates

When transforming a DF to SPDF you are setting the coordinates.

Note - the transformation happens in place!

sfhomes15_sp <- sfhomes15  # Make a copy - why?

class(sfhomes15_sp)  # check the class of the object

coordinates(sfhomes15_sp) <- c('lon','lat')  #  Make it spatial
                                             #  ORDER MATTERS!!

class(sfhomes15_sp)  # check the class of the object

sfhomes15_sp <- sfhomes  # Make a copy - why?

class(sfhomes15_sp)  # check the class of the object

## [1] "data.frame"

coordinates(sfhomes15_sp) <- c('lon','lat')  #  Make it spatial - ORDER MATTERS!!

class(sfhomes15_sp)  # check the class of the object

## [1] "SpatialPointsDataFrame"
## attr(,"package")
## [1] "sp"

You transformed a data frame to an SPDF using:

coordinates(sfhomes15_sp) <- c('lon','lat')

Now try this:

coordinates(sfhomes15_sp)

coordinates(sfhomes15_sp)

##                lon      lat
##     [1,] -122.4660 37.72416
##     [2,] -122.4544 37.78188
##     [3,] -122.4673 37.77417
##     [4,] -122.5034 37.75042
##     [5,] -122.4853 37.78259
##     [6,] -122.4824 37.74192
##     [7,] -122.4665 37.73471
##     [8,] -122.4010 37.72049
##     [9,] -122.4710 37.77409
##    [10,] -122.4176 37.75749
##    [11,] -122.4665 37.77795
##    [12,] -122.4111 37.74450
##    [13,] -122.4865 37.74895
##    [14,] -122.4425 37.77948
##    [15,] -122.4786 37.76188
##    [16,] -122.4957 37.77254
##    [17,] -122.4131 37.80550
##    [18,] -122.4533 37.78982
##    [19,] -122.4677 37.74954
##    [20,] -122.4885 37.73842
##    [21,] -122.4398 37.80320
##    [22,] -122.3889 37.74083
##    [23,] -122.4361 37.74090
##    [24,] -122.4741 37.73601
##    [25,] -122.3922 37.78607
##    [26,] -122.4109 37.78489
##    [27,] -122.5051 37.76011
##    [28,] -122.4063 37.70855
##    [29,] -122.4972 37.77808
##    [30,] -122.4070 37.77571
##    [31,] -122.4362 37.72982
##    [32,] -122.4127 37.79953
##    [33,] -122.4300 37.77660
##    [34,] -122.4444 37.76104
##    [35,] -122.3965 37.75920
##    [36,] -122.4141 37.77641
##    [37,] -122.4187 37.74791
##    [38,] -122.4785 37.75588
##    [39,] -122.4366 37.77051
##    [40,] -122.3957 37.78682
##    [41,] -122.4498 37.72932
##    [42,] -122.3954 37.75793
##    [43,] -122.4920 37.75764
##    [44,] -122.4750 37.75313
##    [45,] -122.4262 37.77009
##    [46,] -122.4257 37.76385
##    [47,] -122.4966 37.74518
##    [48,] -122.4055 37.80424
##    [49,] -122.4523 37.77239
##    [50,] -122.4338 37.75102
##    [51,] -122.4914 37.77273
##    [52,] -122.4642 37.74756
##    [53,] -122.4684 37.70943
##    [54,] -122.4165 37.75900
##    [55,] -122.5072 37.75912
##    [56,] -122.4783 37.76074
##    [57,] -122.4236 37.77750
##    [58,] -122.4615 37.72611
##    [59,] -122.4696 37.71758
##    [60,] -122.4935 37.75606
##    [61,] -122.4977 37.76280
##    [62,] -122.4443 37.77486
##    [63,] -122.4849 37.76211
##    [64,] -122.4766 37.78218
##    [65,] -122.4787 37.75199
##    [66,] -122.4015 37.75647
##    [67,] -122.4843 37.73922
##    [68,] -122.4645 37.74101
##    [69,] -122.4396 37.74598
##    [70,] -122.4416 37.77194
##    [71,] -122.4229 37.80586
##    [72,] -122.4605 37.72257
##    [73,] -122.4380 37.74101
##    [74,] -122.3918 37.77899
##    [75,] -122.4508 37.71993
##    [76,] -122.3942 37.77181
##    [77,] -122.4234 37.77422
##    [78,] -122.4647 37.71645
##    [79,] -122.4754 37.71518
##    [80,] -122.3995 37.75597
##    [81,] -122.4172 37.79608
##    [82,] -122.4085 37.72821
##    [83,] -122.4466 37.76526
##    [84,] -122.4252 37.78931
##    [85,] -122.4210 37.75876
##    [86,] -122.4773 37.75511
##    [87,] -122.4524 37.71039
##    [88,] -122.4345 37.73827
##    [89,] -122.4870 37.74699
##    [90,] -122.4149 37.79362
##    [91,] -122.4012 37.79226
##    [92,] -122.4370 37.74020
##    [93,] -122.4370 37.75217
##    [94,] -122.3904 37.75368
##    [95,] -122.4395 37.75554
##    [96,] -122.4312 37.79505
##    [97,] -122.4647 37.71707
##    [98,] -122.4437 37.78881
##    [99,] -122.4344 37.78622
##   [100,] -122.4558 37.76489
##   [101,] -122.4533 37.73519
##   [102,] -122.4522 37.71156
##   [103,] -122.4346 37.75021
##   [104,] -122.4155 37.75369
##   [105,] -122.4301 37.78409
##   [106,] -122.4640 37.76523
##   [107,] -122.4854 37.75434
##   [108,] -122.4545 37.78186
##   [109,] -122.4669 37.75265
##   [110,] -122.4175 37.73951
##   [111,] -122.3989 37.76034
##   [112,] -122.4213 37.79018
##   [113,] -122.3991 37.78660
##   [114,] -122.4128 37.80494
##   [115,] -122.4738 37.75122
##   [116,] -122.4098 37.70996
##   [117,] -122.4285 37.75510
##   [118,] -122.4081 37.71601
##   [119,] -122.4658 37.76085
##   [120,] -122.4009 37.73248
##   [121,] -122.4851 37.74278
##   [122,] -122.4961 37.77799
##   [123,] -122.4138 37.75804
##   [124,] -122.4199 37.73126
##   [125,] -122.4307 37.76047
##   [126,] -122.4500 37.76787
##   [127,] -122.3848 37.75001
##   [128,] -122.4687 37.71807
##   [129,] -122.4274 37.77132
##   [130,] -122.4048 37.77883
##   [131,] -122.4834 37.75650
##   [132,] -122.3892 37.76399
##   [133,] -122.4782 37.75839
##   [134,] -122.4844 37.77949
##   [135,] -122.4675 37.77652
##   [136,] -122.4181 37.74544
##   [137,] -122.4379 37.77336
##   [138,] -122.4791 37.78131
##   [139,] -122.4593 37.71286
##   [140,] -122.4505 37.76682
##   [141,] -122.4153 37.77613
##   [142,] -122.4902 37.73600
##   [143,] -122.4012 37.71432
##   [144,] -122.4900 37.74451
##   [145,] -122.4170 37.73112
##   [146,] -122.3957 37.78009
##   [147,] -122.4259 37.71117
##   [148,] -122.4372 37.74161
##   [149,] -122.3973 37.76407
##   [150,] -122.4926 37.77496
##   [151,] -122.4246 37.71055
##   [152,] -122.4450 37.77005
##   [153,] -122.3957 37.72696
##   [154,] -122.4305 37.79001
##   [155,] -122.4309 37.76080
##   [156,] -122.4249 37.76548
##   [157,] -122.4442 37.78391
##   [158,] -122.4016 37.73361
##   [159,] -122.4137 37.79668
##   [160,] -122.4868 37.77458
##   [161,] -122.4020 37.76116
##   [162,] -122.4221 37.77111
##   [163,] -122.4585 37.73047
##   [164,] -122.3991 37.78318
##   [165,] -122.4340 37.78858
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##   [640,] -122.4038 37.80131
##   [641,] -122.4603 37.75534
##   [642,] -122.4856 37.73124
##   [643,] -122.3941 37.77470
##   [644,] -122.4303 37.75128
##   [645,] -122.4310 37.72356
##   [646,] -122.4225 37.78676
##   [647,] -122.4116 37.79687
##   [648,] -122.4293 37.79020
##   [649,] -122.4173 37.74478
##   [650,] -122.4230 37.79056
##   [651,] -122.4970 37.74384
##   [652,] -122.4350 37.79214
##   [653,] -122.4174 37.79823
##   [654,] -122.4069 37.80092
##   [655,] -122.4543 37.71990
##   [656,] -122.4676 37.71048
##   [657,] -122.4439 37.75226
##   [658,] -122.3919 37.78868
##   [659,] -122.3886 37.77159
##   [660,] -122.4097 37.77681
##   [661,] -122.4243 37.76336
##   [662,] -122.5066 37.74980
##   [663,] -122.4327 37.71788
##   [664,] -122.4357 37.71030
##   [665,] -122.4261 37.74349
##   [666,] -122.4727 37.74147
##   [667,] -122.4016 37.77636
##   [668,] -122.3904 37.78139
##   [669,] -122.4332 37.73645
##   [670,] -122.4738 37.72814
##   [671,] -122.4026 37.78273
##   [672,] -122.4165 37.74792
##   [673,] -122.4159 37.79593
##   [674,] -122.5088 37.77537
##   [675,] -122.4558 37.72146
##   [676,] -122.5104 37.77404
##   [677,] -122.4865 37.75436
##   [678,] -122.4642 37.78379
##   [679,] -122.4150 37.79720
##   [680,] -122.4261 37.75756
##   [681,] -122.3974 37.76455
##   [682,] -122.4361 37.75773
##   [683,] -122.4458 37.74398
##   [684,] -122.4386 37.79838
##   [685,] -122.3949 37.76308
##   [686,] -122.4166 37.73981
##   [687,] -122.4849 37.75560
##   [688,] -122.4169 37.77301
##   [689,] -122.3937 37.78702
##   [690,] -122.4188 37.77159
##   [691,] -122.3887 37.73774
##   [692,] -122.3896 37.78801
##   [693,] -122.4679 37.76113
##   [694,] -122.3956 37.77723
##   [695,] -122.4607 37.72536
##   [696,] -122.4212 37.80533
##   [697,] -122.4505 37.71653
##   [698,] -122.4352 37.72532
##   [699,] -122.4384 37.77139
##   [700,] -122.4164 37.74580
##   [701,] -122.4365 37.76181
##   [702,] -122.4089 37.79323
##   [703,] -122.4021 37.78077
##   [704,] -122.4873 37.77829
##   [705,] -122.4147 37.74113
##   [706,] -122.5078 37.76165
##   [707,] -122.4399 37.71349
##   [708,] -122.4553 37.71292
##   [709,] -122.4400 37.78935
##   [710,] -122.4606 37.76360
##   [711,] -122.4974 37.77916
##   [712,] -122.4015 37.72055
##   [713,] -122.4968 37.74261
##   [714,] -122.4392 37.80371
##   [715,] -122.4393 37.75689
##   [716,] -122.4255 37.72965
##   [717,] -122.5009 37.76023
##   [718,] -122.4103 37.71464
##   [719,] -122.4275 37.74336
##   [720,] -122.4157 37.79637
##   [721,] -122.4332 37.77035
##   [722,] -122.5086 37.77873
##   [723,] -122.5040 37.77506
##   [724,] -122.4160 37.72585
##   [725,] -122.4966 37.72999
##   [726,] -122.4396 37.75859
##   [727,] -122.4358 37.78941
##   [728,] -122.4244 37.78587
##   [729,] -122.4466 37.75998
##   [730,] -122.4806 37.73933
##   [731,] -122.4383 37.70970
##   [732,] -122.4014 37.72736
##   [733,] -122.4020 37.75390
##   [734,] -122.3977 37.75782
##   [735,] -122.4418 37.71189
##   [736,] -122.4546 37.76467
##   [737,] -122.4861 37.73524
##   [738,] -122.3940 37.78565
##   [739,] -122.4409 37.78482
##   [740,] -122.4341 37.72610
##   [741,] -122.4131 37.80039
##   [742,] -122.4354 37.75098
##   [743,] -122.4138 37.73940
##   [744,] -122.4402 37.71792
##   [745,] -122.4600 37.72444
##   [746,] -122.4578 37.75273
##   [747,] -122.4043 37.75973
##   [748,] -122.3861 37.72113
##   [749,] -122.4644 37.77771
##   [750,] -122.4863 37.74591
##   [751,] -122.4312 37.78032
##   [752,] -122.4428 37.71197
##   [753,] -122.4308 37.78100
##   [754,] -122.4578 37.70838
##   [755,] -122.4903 37.77272
##   [756,] -122.4460 37.74744
##   [757,] -122.4814 37.77408
##   [758,] -122.4695 37.71537
##   [759,] -122.4795 37.77722
##   [760,] -122.4170 37.72644
##   [761,] -122.3989 37.78577
##   [762,] -122.4085 37.74409
##   [763,] -122.4621 37.77656
##   [764,] -122.4710 37.72292
##   [765,] -122.4106 37.75455
##   [766,] -122.4517 37.78385
##   [767,] -122.3909 37.78690
##   [768,] -122.4096 37.72803
##   [769,] -122.4396 37.77926
##   [770,] -122.3947 37.77419
##   [771,] -122.4080 37.80389
##   [772,] -122.4004 37.72333
##   [773,] -122.4399 37.76730
##   [774,] -122.3883 37.73754
##   [775,] -122.4333 37.75642
##   [776,] -122.4767 37.75347
##   [777,] -122.3962 37.77393
##   [778,] -122.4476 37.75786
##   [779,] -122.4868 37.74478
##   [780,] -122.4059 37.75194
##   [781,] -122.4323 37.72323
##   [782,] -122.4176 37.76285
##   [783,] -122.4620 37.72948
##   [784,] -122.5076 37.75054
##   [785,] -122.4199 37.77606
##   [786,] -122.4420 37.76088
##   [787,] -122.4541 37.73382
##   [788,] -122.3960 37.78175
##   [789,] -122.4322 37.72290
##   [790,] -122.4806 37.74044
##   [791,] -122.3974 37.78575
##   [792,] -122.4130 37.74456
##   [793,] -122.4405 37.75796
##   [794,] -122.3992 37.75640
##   [795,] -122.4587 37.74523
##   [796,] -122.4266 37.75187
##   [797,] -122.4021 37.78077
##   [798,] -122.4262 37.77048
##   [799,] -122.4360 37.72409
##   [800,] -122.4521 37.73012
##   [801,] -122.4342 37.78664
##   [802,] -122.4951 37.76415
##   [803,] -122.4056 37.73172
##   [804,] -122.4254 37.74954
##   [805,] -122.3890 37.72564
##   [806,] -122.4740 37.75418
##   [807,] -122.4747 37.73359
##   [808,] -122.4380 37.75242
##   [809,] -122.4017 37.71953
##   [810,] -122.4912 37.75970
##   [811,] -122.4575 37.74586
##   [812,] -122.4446 37.71131
##   [813,] -122.4174 37.79247
##   [814,] -122.4229 37.80046
##   [815,] -122.4473 37.78883
##   [816,] -122.3879 37.72915
##   [817,] -122.3897 37.78278
##   [818,] -122.3876 37.73527
##   [819,] -122.4369 37.72355
##   [820,] -122.4415 37.72446
##   [821,] -122.4413 37.72440
##   [822,] -122.4524 37.75013
##   [823,] -122.4933 37.74385
##   [824,] -122.4551 37.70830
##   [825,] -122.4458 37.79878
##   [826,] -122.3974 37.73021
##   [827,] -122.4715 37.73787
##   [828,] -122.4558 37.72327
##   [829,] -122.4889 37.77354
##   [830,] -122.4732 37.74178
##   [831,] -122.4846 37.75243
##   [832,] -122.4448 37.76229
##   [833,] -122.4378 37.72485
##   [834,] -122.4236 37.76506
##   [835,] -122.4363 37.75494
##   [836,] -122.4301 37.79705
##   [837,] -122.4070 37.77816
##   [838,] -122.4904 37.76412
##   [839,] -122.4857 37.75232
##   [840,] -122.3978 37.79763
##   [841,] -122.4166 37.75254
##   [842,] -122.4764 37.77958
##   [843,] -122.4069 37.75179
##   [844,] -122.4790 37.75201
##   [845,] -122.4469 37.78924
##   [846,] -122.4596 37.71771
##   [847,] -122.4045 37.75737
##   [848,] -122.4051 37.72410
##   [849,] -122.4219 37.74655
##   [850,] -122.4338 37.77036
##   [851,] -122.4747 37.73894
##   [852,] -122.4473 37.77331
##   [853,] -122.4330 37.73489
##   [854,] -122.4397 37.77741
##   [855,] -122.4047 37.72586
##   [856,] -122.4899 37.75780
##   [857,] -122.4458 37.72722
##   [858,] -122.4903 37.76330
##   [859,] -122.4538 37.71944
##   [860,] -122.4762 37.76042
##   [861,] -122.4508 37.73988
##   [862,] -122.3914 37.78451
##   [863,] -122.4327 37.72702
##   [864,] -122.4326 37.74229
##   [865,] -122.4704 37.78480
##   [866,] -122.4866 37.78083
##   [867,] -122.4379 37.74059
##   [868,] -122.4505 37.71022
##   [869,] -122.4453 37.79660
##   [870,] -122.4945 37.77681
##   [871,] -122.4444 37.80057
##   [872,] -122.4242 37.79788
##   [873,] -122.4661 37.75638
##   [874,] -122.4909 37.74120
##   [875,] -122.4341 37.77222
##   [876,] -122.4139 37.74492
##   [877,] -122.4786 37.77400
##   [878,] -122.4083 37.79385
##   [879,] -122.4007 37.75253
##   [880,] -122.4139 37.77622
##   [881,] -122.3980 37.76458
##   [882,] -122.4430 37.77745
##   [883,] -122.4951 37.76395
##   [884,] -122.4179 37.76435
##   [885,] -122.4723 37.75826
##   [886,] -122.4209 37.74043
##   [887,] -122.5079 37.76124
##   [888,] -122.4509 37.76976
##   [889,] -122.4008 37.75266
##   [890,] -122.3904 37.78271
##   [891,] -122.4716 37.75880
##   [892,] -122.4269 37.72559
##   [893,] -122.4329 37.73429
##   [894,] -122.3906 37.72087
##   [895,] -122.4291 37.78890
##   [896,] -122.4681 37.75503
##   [897,] -122.4087 37.74137
##   [898,] -122.4832 37.76281
##   [899,] -122.4151 37.78524
##   [900,] -122.4452 37.78054
##   [901,] -122.4023 37.75871
##   [902,] -122.4200 37.74480
##   [903,] -122.4521 37.71151
##   [904,] -122.3844 37.72996
##   [905,] -122.4233 37.73974
##   [906,] -122.3919 37.78868
##   [907,] -122.4167 37.76105
##   [908,] -122.4757 37.78472
##   [909,] -122.4357 37.73695
##   [910,] -122.4121 37.77717
##   [911,] -122.4488 37.76856
##   [912,] -122.3912 37.78435
##   [913,] -122.4170 37.74527
##   [914,] -122.4240 37.75895
##   [915,] -122.4808 37.74975
##   [916,] -122.3956 37.73229
##   [917,] -122.4959 37.77553
##   [918,] -122.4357 37.76031
##   [919,] -122.4316 37.76576
##   [920,] -122.4086 37.71069
##   [921,] -122.3896 37.78063
##   [922,] -122.4583 37.78441
##   [923,] -122.4694 37.75795
##   [924,] -122.4499 37.72129
##   [925,] -122.4109 37.76451
##   [926,] -122.4463 37.77655
##   [927,] -122.4008 37.76912
##   [928,] -122.4424 37.71523
##   [929,] -122.4224 37.77669
##   [930,] -122.4832 37.74757
##   [931,] -122.4875 37.76476
##   [932,] -122.4092 37.75983
##   [933,] -122.3897 37.73655
##   [934,] -122.4608 37.73207
##   [935,] -122.4050 37.73021
##   [936,] -122.4808 37.76472
##   [937,] -122.4841 37.70987
##   [938,] -122.4224 37.75577
##   [939,] -122.4379 37.73134
##   [940,] -122.4656 37.78000
##   [941,] -122.5011 37.75794
##   [942,] -122.4217 37.79292
##   [943,] -122.4260 37.72238
##   [944,] -122.4968 37.77865
##   [945,] -122.4022 37.77608
##   [946,] -122.4440 37.78444
##   [947,] -122.4338 37.71974
##   [948,] -122.4217 37.74954
##   [949,] -122.4436 37.71335
##   [950,] -122.4151 37.78524
##   [951,] -122.4853 37.76240
##   [952,] -122.3677 37.72817
##   [953,] -122.4132 37.79284
##   [954,] -122.4894 37.75984
##   [955,] -122.4303 37.72597
##   [956,] -122.4126 37.72905
##   [957,] -122.3904 37.76258
##   [958,] -122.4098 37.78841
##   [959,] -122.4996 37.75848
##   [960,] -122.4250 37.77402
##   [961,] -122.3980 37.76410
##   [962,] -122.4706 37.73978
##   [963,] -122.4554 37.77608
##   [964,] -122.4276 37.75062
##   [965,] -122.5079 37.76383
##   [966,] -122.5075 37.74749
##   [967,] -122.3937 37.78702
##   [968,] -122.5044 37.74262
##   [969,] -122.4415 37.74544
##   [970,] -122.4129 37.80619
##   [971,] -122.4075 37.72452
##   [972,] -122.4427 37.78896
##   [973,] -122.3848 37.73775
##   [974,] -122.4380 37.72624
##   [975,] -122.4599 37.72285
##   [976,] -122.4924 37.73886
##   [977,] -122.4171 37.74125
##   [978,] -122.4569 37.73442
##   [979,] -122.4480 37.71786
##   [980,] -122.4735 37.73207
##   [981,] -122.4570 37.74439
##   [982,] -122.4888 37.75675
##   [983,] -122.4260 37.75159
##   [984,] -122.4430 37.74641
##   [985,] -122.4165 37.77528
##   [986,] -122.5034 37.77565
##   [987,] -122.4917 37.73590
##   [988,] -122.3903 37.73120
##   [989,] -122.4876 37.75598
##   [990,] -122.4929 37.76308
##   [991,] -122.4700 37.74407
##   [992,] -122.4250 37.77726
##   [993,] -122.3934 37.77764
##   [994,] -122.4274 37.73322
##   [995,] -122.3996 37.77438
##   [996,] -122.4483 37.72858
##   [997,] -122.3909 37.75967
##   [998,] -122.4479 37.77113
##   [999,] -122.4036 37.71297
##  [1000,] -122.4635 37.77400
##  [1001,] -122.3919 37.78868
##  [1002,] -122.4392 37.78412
##  [1003,] -122.3745 37.73161
##  [1004,] -122.4340 37.78723
##  [1005,] -122.4156 37.75382
##  [1006,] -122.4320 37.78195
##  [1007,] -122.4031 37.71429
##  [1008,] -122.4156 37.79695
##  [1009,] -122.3922 37.78607
##  [1010,] -122.4817 37.74764
##  [1011,] -122.4369 37.71662
##  [1012,] -122.3903 37.75503
##  [1013,] -122.4405 37.80417
##  [1014,] -122.4698 37.76292
##  [1015,] -122.4436 37.76421
##  [1016,] -122.4771 37.73164
##  [1017,] -122.4249 37.76548
##  [1018,] -122.4452 37.76906
##  [1019,] -122.4796 37.76183
##  [1020,] -122.4322 37.75241
##  [1021,] -122.4323 37.76242
##  [1022,] -122.4715 37.71944
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##  [1024,] -122.5082 37.75360
##  [1025,] -122.4262 37.73504
##  [1026,] -122.4025 37.76116
##  [1027,] -122.4244 37.78587
##  [1028,] -122.3904 37.78139
##  [1029,] -122.4521 37.71455
##  [1030,] -122.5060 37.74905
##  [1031,] -122.4020 37.72827
##  [1032,] -122.4857 37.75218
##  [1033,] -122.4225 37.78676
##  [1034,] -122.4844 37.77980
##  [1035,] -122.4878 37.75015
##  [1036,] -122.4097 37.75549
##  [1037,] -122.4191 37.72612
##  [1038,] -122.4215 37.79954
##  [1039,] -122.4062 37.73202
##  [1040,] -122.4882 37.75958
##  [1041,] -122.4151 37.78524
##  [1042,] -122.3942 37.77181
##  [1043,] -122.4500 37.77800
##  [1044,] -122.4171 37.75186
##  [1045,] -122.4707 37.77544
##  [1046,] -122.4301 37.71696
##  [1047,] -122.4515 37.78021
##  [1048,] -122.4164 37.74889
##  [1049,] -122.4327 37.72504
##  [1050,] -122.4816 37.77809
##  [1051,] -122.4586 37.76543
##  [1052,] -122.3850 37.73390
##  [1053,] -122.3971 37.77626
##  [1054,] -122.5057 37.74758
##  [1055,] -122.4558 37.77922
##  [1056,] -122.3909 37.78690
##  [1057,] -122.4425 37.80502
##  [1058,] -122.4451 37.75450
##  [1059,] -122.4167 37.73422
##  [1060,] -122.4041 37.80347
##  [1061,] -122.4569 37.74354
##  [1062,] -122.4379 37.76025
##  [1063,] -122.4965 37.75276
##  [1064,] -122.4127 37.78995
##  [1065,] -122.4736 37.78698
##  [1066,] -122.4015 37.71913
##  [1067,] -122.4451 37.70862
##  [1068,] -122.4191 37.74379
##  [1069,] -122.4219 37.79814
##  [1070,] -122.4669 37.75234
##  [1071,] -122.4394 37.78124
##  [1072,] -122.4903 37.74116
##  [1073,] -122.5048 37.74766
##  [1074,] -122.4646 37.77932
##  [1075,] -122.3989 37.73266
##  [1076,] -122.4601 37.77531
##  [1077,] -122.4356 37.78512
##  [1078,] -122.4744 37.77577
##  [1079,] -122.4343 37.72345
##  [1080,] -122.3864 37.71757
##  [1081,] -122.4122 37.75293
##  [1082,] -122.4421 37.79884
##  [1083,] -122.4358 37.75095
##  [1084,] -122.4083 37.80179
##  [1085,] -122.4358 37.76195
##  [1086,] -122.3930 37.73297
##  [1087,] -122.4165 37.77528
##  [1088,] -122.4607 37.75559
##  [1089,] -122.4354 37.73548
##  [1090,] -122.4006 37.71578
##  [1091,] -122.4718 37.76145
##  [1092,] -122.4220 37.80185
##  [1093,] -122.4402 37.74892
##  [1094,] -122.4168 37.79879
##  [1095,] -122.4417 37.73374
##  [1096,] -122.4077 37.75106
##  [1097,] -122.4937 37.77999
##  [1098,] -122.4379 37.77734
##  [1099,] -122.4227 37.74574
##  [1100,] -122.4735 37.75852
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##  [1701,] -122.4240 37.78482
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##  [1713,] -122.4544 37.78034
##  [1714,] -122.4617 37.75532
##  [1715,] -122.4225 37.78676
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##  [1891,] -122.4924 37.74393
##  [1892,] -122.4089 37.79323
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##  [1894,] -122.4661 37.76543
##  [1895,] -122.4032 37.71631
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##  [1897,] -122.4054 37.79857
##  [1898,] -122.4130 37.80169
##  [1899,] -122.4653 37.75417
##  [1900,] -122.4232 37.72677
##  [1901,] -122.4376 37.76780
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##  [1903,] -122.4325 37.71009
##  [1904,] -122.4733 37.78191
##  [1905,] -122.4891 37.76048
##  [1906,] -122.4456 37.79169
##  [1907,] -122.4079 37.78298
##  [1908,] -122.4460 37.77545
##  [1909,] -122.4173 37.80080
##  [1910,] -122.4513 37.74778
##  [1911,] -122.4050 37.75286
##  [1912,] -122.3996 37.71188
##  [1913,] -122.4146 37.74714
##  [1914,] -122.5013 37.75987
##  [1915,] -122.4698 37.77829
##  [1916,] -122.4323 37.72112
##  [1917,] -122.4064 37.74623
##  [1918,] -122.4701 37.77907
##  [1919,] -122.4665 37.76272
##  [1920,] -122.4139 37.73105
##  [1921,] -122.4721 37.74170
##  [1922,] -122.4888 37.75682
##  [1923,] -122.4116 37.77806
##  [1924,] -122.4299 37.76869
##  [1925,] -122.3977 37.73463
##  [1926,] -122.3937 37.78702
##  [1927,] -122.4504 37.75932
##  [1928,] -122.4826 37.71334
##  [1929,] -122.4187 37.74860
##  [1930,] -122.4656 37.71691
##  [1931,] -122.4575 37.77698
##  [1932,] -122.4300 37.71763
##  [1933,] -122.4261 37.77170
##  [1934,] -122.4583 37.71204
##  [1935,] -122.4253 37.72096
##  [1936,] -122.4974 37.76426
##  [1937,] -122.4475 37.76576
##  [1938,] -122.3889 37.73586
##  [1939,] -122.4648 37.73726
##  [1940,] -122.4017 37.73369
##  [1941,] -122.4031 37.79058
##  [1942,] -122.4680 37.72672
##  [1943,] -122.4252 37.77406
##  [1944,] -122.4041 37.80347
##  [1945,] -122.4579 37.72223
##  [1946,] -122.3989 37.78577
##  [1947,] -122.4513 37.78449
##  [1948,] -122.5035 37.75225
##  [1949,] -122.4732 37.72275
##  [1950,] -122.4103 37.72705
##  [1951,] -122.4218 37.74083
##  [1952,] -122.4718 37.74342
##  [1953,] -122.4918 37.76140
##  [1954,] -122.4575 37.71256
##  [1955,] -122.4422 37.71039
##  [1956,] -122.4365 37.75643
##  [1957,] -122.4736 37.77946
##  [1958,] -122.3934 37.77764
##  [1959,] -122.4636 37.73325
##  [1960,] -122.4683 37.75696
##  [1961,] -122.4224 37.75417
##  [1962,] -122.3880 37.72979
##  [1963,] -122.4129 37.75398
##  [1964,] -122.3910 37.78938
##  [1965,] -122.4671 37.72222
##  [1966,] -122.3865 37.72535
##  [1967,] -122.3943 37.78442
##  [1968,] -122.4318 37.79399
##  [1969,] -122.4555 37.78533
##  [1970,] -122.4343 37.75100
##  [1971,] -122.4484 37.75985
##  [1972,] -122.4260 37.76887
##  [1973,] -122.4055 37.80424
##  [1974,] -122.4224 37.80096
##  [1975,] -122.4135 37.74803
##  [1976,] -122.4626 37.73517
##  [1977,] -122.4818 37.77393
##  [1978,] -122.4101 37.78945
##  [1979,] -122.4734 37.77807
##  [1980,] -122.4318 37.76052
##  [1981,] -122.4277 37.72647
##  [1982,] -122.4248 37.76880
##  [1983,] -122.4673 37.75489
##  [1984,] -122.4370 37.74127
##  [1985,] -122.4246 37.75774
##  [1986,] -122.4542 37.77581
##  [1987,] -122.4331 37.78659
##  [1988,] -122.4500 37.75293
##  [1989,] -122.4434 37.73406
##  [1990,] -122.4905 37.76086
##  [1991,] -122.4553 37.78296
##  [1992,] -122.4595 37.70949
##  [1993,] -122.3967 37.73514
##  [1994,] -122.4374 37.73501
##  [1995,] -122.5031 37.75656
##  [1996,] -122.4703 37.73450
##  [1997,] -122.4094 37.77828
##  [1998,] -122.4203 37.77248
##  [1999,] -122.3942 37.77181
##  [2000,] -122.4718 37.75301
##  [2001,] -122.4108 37.74855
##  [2002,] -122.4273 37.79601
##  [2003,] -122.4846 37.75277
##  [2004,] -122.4750 37.75382
##  [2005,] -122.4318 37.77248
##  [2006,] -122.3935 37.71183
##  [2007,] -122.4144 37.80007
##  [2008,] -122.4962 37.75441
##  [2009,] -122.4935 37.74130
##  [2010,] -122.4725 37.75279
##  [2011,] -122.4021 37.78077
##  [2012,] -122.4465 37.74772
##  [2013,] -122.4064 37.75155
##  [2014,] -122.4206 37.72992
##  [2015,] -122.3902 37.72441
##  [2016,] -122.4882 37.77840
##  [2017,] -122.4237 37.73853
##  [2018,] -122.4451 37.75955
##  [2019,] -122.4865 37.75168
##  [2020,] -122.4097 37.75535
##  [2021,] -122.4411 37.80538
##  [2022,] -122.4637 37.73800
##  [2023,] -122.3889 37.75706
##  [2024,] -122.4676 37.71048
##  [2025,] -122.4118 37.79298
##  [2026,] -122.4285 37.72873
##  [2027,] -122.4425 37.79208
##  [2028,] -122.4249 37.79968
##  [2029,] -122.4399 37.72861
##  [2030,] -122.4478 37.76474
##  [2031,] -122.4243 37.79352
##  [2032,] -122.4744 37.77606
##  [2033,] -122.4249 37.76548
##  [2034,] -122.4350 37.76455
##  [2035,] -122.4427 37.76017
##  [2036,] -122.4089 37.77800
##  [2037,] -122.4484 37.71442
##  [2038,] -122.4093 37.71144
##  [2039,] -122.4106 37.77490
##  [2040,] -122.4852 37.78225
##  [2041,] -122.4186 37.73128
##  [2042,] -122.4362 37.74694
##  [2043,] -122.4430 37.80248
##  [2044,] -122.4194 37.80175
##  [2045,] -122.4173 37.76061
##  [2046,] -122.3910 37.78938
##  [2047,] -122.4744 37.78139
##  [2048,] -122.4519 37.78823
##  [2049,] -122.5048 37.74849
##  [2050,] -122.4003 37.71268
##  [2051,] -122.4278 37.73442
##  [2052,] -122.4239 37.76572
##  [2053,] -122.3918 37.77863
##  [2054,] -122.4552 37.76398
##  [2055,] -122.4396 37.74598
##  [2056,] -122.3948 37.74437
##  [2057,] -122.4065 37.78073
##  [2058,] -122.4293 37.71085
##  [2059,] -122.4613 37.78084
##  [2060,] -122.4769 37.75590
##  [2061,] -122.3962 37.77393
##  [2062,] -122.4355 37.79922
##  [2063,] -122.4135 37.78148
##  [2064,] -122.4293 37.76186
##  [2065,] -122.4078 37.71394
##  [2066,] -122.4243 37.75206
##  [2067,] -122.4789 37.74721
##  [2068,] -122.4178 37.76399
##  [2069,] -122.4616 37.72144
##  [2070,] -122.4558 37.77639
##  [2071,] -122.4285 37.73820
##  [2072,] -122.5016 37.75597
##  [2073,] -122.4097 37.77613
##  [2074,] -122.4380 37.80313
##  [2075,] -122.4394 37.80558
##  [2076,] -122.4519 37.78823
##  [2077,] -122.4200 37.72700
##  [2078,] -122.4564 37.78288
##  [2079,] -122.5021 37.77785
##  [2080,] -122.4255 37.73553
##  [2081,] -122.4041 37.80347
##  [2082,] -122.4240 37.75809
##  [2083,] -122.4475 37.75713
##  [2084,] -122.3918 37.77863
##  [2085,] -122.5073 37.75974
##  [2086,] -122.3941 37.77470
##  [2087,] -122.4987 37.73898
##  [2088,] -122.4184 37.78390
##  [2089,] -122.4634 37.78134
##  [2090,] -122.5028 37.75099
##  [2091,] -122.4218 37.75230
##  [2092,] -122.4071 37.80282
##  [2093,] -122.4461 37.71616
##  [2094,] -122.4410 37.76196
##  [2095,] -122.4169 37.76730
##  [2096,] -122.3996 37.73859
##  [2097,] -122.4825 37.73797
##  [2098,] -122.5049 37.74113
##  [2099,] -122.4624 37.71785
##  [2100,] -122.4284 37.76473
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##  [2102,] -122.4258 37.73961
##  [2103,] -122.4392 37.77267
##  [2104,] -122.4041 37.79850
##  [2105,] -122.4326 37.75686
##  [2106,] -122.4293 37.80332
##  [2107,] -122.4513 37.71126
##  [2108,] -122.4425 37.78377
##  [2109,] -122.4373 37.75334
##  [2110,] -122.3986 37.75672
##  [2111,] -122.4589 37.72028
##  [2112,] -122.4259 37.70869
##  [2113,] -122.3922 37.78607
##  [2114,] -122.4055 37.72510
##  [2115,] -122.4259 37.79386
##  [2116,] -122.4882 37.77274
##  [2117,] -122.4242 37.79788
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##  [2119,] -122.4669 37.72041
##  [2120,] -122.4565 37.72347
##  [2121,] -122.4291 37.79541
##  [2122,] -122.3713 37.72830
##  [2123,] -122.4396 37.76686
##  [2124,] -122.4176 37.75052
##  [2125,] -122.5069 37.77181
##  [2126,] -122.4122 37.79293
##  [2127,] -122.4108 37.76409
##  [2128,] -122.4331 37.78659
##  [2129,] -122.3936 37.78370
##  [2130,] -122.4286 37.74405
##  [2131,] -122.5006 37.74972
##  [2132,] -122.4452 37.74643
##  [2133,] -122.4884 37.77962
##  [2134,] -122.4581 37.77455
##  [2135,] -122.4774 37.77835
##  [2136,] -122.4265 37.71884
##  [2137,] -122.4019 37.77323
##  [2138,] -122.4794 37.75467
##  [2139,] -122.4456 37.75932
##  [2140,] -122.4378 37.74841
##  [2141,] -122.4878 37.77331
##  [2142,] -122.4756 37.77719
##  [2143,] -122.4588 37.74588
##  [2144,] -122.3927 37.73750
##  [2145,] -122.5024 37.76016
##  [2146,] -122.4648 37.72144
##  [2147,] -122.4897 37.76398
##  [2148,] -122.4069 37.76239
##  [2149,] -122.4562 37.73394
##  [2150,] -122.4418 37.76392
##  [2151,] -122.4966 37.73314
##  [2152,] -122.4256 37.76092
##  [2153,] -122.4331 37.76004
##  [2154,] -122.4234 37.79343
##  [2155,] -122.4596 37.71980
##  [2156,] -122.4398 37.80327
##  [2157,] -122.4443 37.71172
##  [2158,] -122.4342 37.72313
##  [2159,] -122.4335 37.75350
##  [2160,] -122.3771 37.73247
##  [2161,] -122.4685 37.73137
##  [2162,] -122.4903 37.74837
##  [2163,] -122.4716 37.78318
##  [2164,] -122.4025 37.71259
##  [2165,] -122.4281 37.72447
##  [2166,] -122.3949 37.75891
##  [2167,] -122.4749 37.78333
##  [2168,] -122.4331 37.79852
##  [2169,] -122.3895 37.76389
##  [2170,] -122.4021 37.78077
##  [2171,] -122.4677 37.74367
##  [2172,] -122.4512 37.75202
##  [2173,] -122.4694 37.75481
##  [2174,] -122.4576 37.73725
##  [2175,] -122.4383 37.70836
##  [2176,] -122.4133 37.80106
##  [2177,] -122.4341 37.75668
##  [2178,] -122.4149 37.79362
##  [2179,] -122.4483 37.74076
##  [2180,] -122.4739 37.72616
##  [2181,] -122.4268 37.72884
##  [2182,] -122.5072 37.77505
##  [2183,] -122.4384 37.77898
##  [2184,] -122.4324 37.74633
##  [2185,] -122.4439 37.76607
##  [2186,] -122.4841 37.74518
##  [2187,] -122.5061 37.75924
##  [2188,] -122.4388 37.77344
##  [2189,] -122.4307 37.74013
##  [2190,] -122.4332 37.78181
##  [2191,] -122.4999 37.74411
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##  [2195,] -122.4916 37.74397
##  [2196,] -122.4061 37.70962
##  [2197,] -122.3922 37.78607
##  [2198,] -122.5039 37.77369
##  [2199,] -122.4743 37.76486
##  [2200,] -122.4663 37.74406
##  [2201,] -122.4517 37.71816
##  [2202,] -122.4081 37.77232
##  [2203,] -122.4214 37.78139
##  [2204,] -122.4921 37.78272
##  [2205,] -122.4632 37.76120
##  [2206,] -122.4295 37.79949
##  [2207,] -122.3991 37.78318
##  [2208,] -122.4065 37.79962
##  [2209,] -122.4456 37.80316
##  [2210,] -122.4277 37.80157
##  [2211,] -122.4242 37.78675
##  [2212,] -122.4760 37.78320
##  [2213,] -122.4240 37.78482
##  [2214,] -122.4329 37.75273
##  [2215,] -122.3894 37.75453
##  [2216,] -122.4440 37.75348
##  [2217,] -122.3942 37.76256
##  [2218,] -122.4077 37.78320
##  [2219,] -122.4250 37.72284
##  [2220,] -122.3957 37.76147
##  [2221,] -122.4977 37.78117
##  [2222,] -122.4180 37.72744
##  [2223,] -122.4421 37.74467
##  [2224,] -122.5054 37.74818
##  [2225,] -122.4348 37.71949
##  [2226,] -122.4256 37.74432
##  [2227,] -122.4287 37.75861
##  [2228,] -122.3989 37.78577
##  [2229,] -122.4997 37.76085
##  [2230,] -122.4481 37.77302
##  [2231,] -122.4253 37.76868
##  [2232,] -122.4228 37.74828
##  [2233,] -122.4860 37.78709
##  [2234,] -122.4147 37.79007
##  [2235,] -122.4374 37.73367
##  [2236,] -122.4600 37.71981
##  [2237,] -122.3954 37.75793
##  [2238,] -122.3968 37.77945
##  [2239,] -122.4313 37.78758
##  [2240,] -122.4043 37.80443
##  [2241,] -122.4517 37.70873
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##  [2243,] -122.4217 37.74186
##  [2244,] -122.3961 37.73352
##  [2245,] -122.4143 37.71265
##  [2246,] -122.4125 37.76307
##  [2247,] -122.4784 37.78459
##  [2248,] -122.4045 37.79929
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##  [2250,] -122.3852 37.73858
##  [2251,] -122.4392 37.71493
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##  [2253,] -122.4883 37.75837
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##  [2257,] -122.4414 37.77709
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## [18713,] -122.4190 37.80173
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## [19580,] -122.4325 37.74359
## [19581,] -122.4027 37.73831
## [19582,] -122.5079 37.75376
## [19583,] -122.4024 37.75621
## [19584,] -122.4064 37.71849
## [19585,] -122.4309 37.79412
## [19586,] -122.4574 37.71990
## [19587,] -122.4627 37.76275
## [19588,] -122.5081 37.75585
## [19589,] -122.5058 37.75132
## [19590,] -122.5066 37.74892
## [19591,] -122.4677 37.75720
## [19592,] -122.4065 37.74508
## [19593,] -122.4069 37.79582
## [19594,] -122.4965 37.75172
## [19595,] -122.4808 37.75869
## [19596,] -122.4912 37.74517
## [19597,] -122.4222 37.80247
## [19598,] -122.4380 37.74101
## [19599,] -122.3934 37.75213
## [19600,] -122.5059 37.75633
## [19601,] -122.4424 37.74562
## [19602,] -122.4197 37.76289
## [19603,] -122.4464 37.76599
## [19604,] -122.4125 37.70921
## [19605,] -122.4347 37.74458
## [19606,] -122.3976 37.77792
## [19607,] -122.4909 37.78111
## [19608,] -122.4762 37.74531
## [19609,] -122.4184 37.79156
## [19610,] -122.4098 37.78841
## [19611,] -122.4258 37.77299
## [19612,] -122.4989 37.74702
## [19613,] -122.4762 37.78505
## [19614,] -122.4416 37.76493
## [19615,] -122.4448 37.77005
## [19616,] -122.4077 37.72642
## [19617,] -122.4833 37.73144
## [19618,] -122.4155 37.71123
## [19619,] -122.4358 37.80525
## [19620,] -122.4960 37.75209
## [19621,] -122.4532 37.73218
## [19622,] -122.5027 37.75593
## [19623,] -122.4662 37.74789
## [19624,] -122.4315 37.72662
## [19625,] -122.4106 37.79568
## [19626,] -122.4348 37.74426
## [19627,] -122.4596 37.78342
## [19628,] -122.4494 37.73987
## [19629,] -122.4147 37.71421
## [19630,] -122.5059 37.77887
## [19631,] -122.4978 37.75916
## [19632,] -122.4969 37.73252
## [19633,] -122.4176 37.77147
## [19634,] -122.3950 37.72742
## [19635,] -122.4661 37.75019
## [19636,] -122.4060 37.76384
## [19637,] -122.4222 37.75260
## [19638,] -122.4295 37.79068
## [19639,] -122.4439 37.71414
## [19640,] -122.4690 37.78211
## [19641,] -122.3919 37.78868
## [19642,] -122.4139 37.79490
## [19643,] -122.4679 37.77561
## [19644,] -122.4687 37.71174
## [19645,] -122.4137 37.79099
## [19646,] -122.4207 37.76391
## [19647,] -122.4509 37.74841
## [19648,] -122.4430 37.74641
## [19649,] -122.4588 37.71275
## [19650,] -122.5053 37.74132
## [19651,] -122.4415 37.80055
## [19652,] -122.4056 37.80110
## [19653,] -122.3904 37.78271
## [19654,] -122.4292 37.79579
## [19655,] -122.4119 37.73638
## [19656,] -122.4438 37.77351
## [19657,] -122.4153 37.79987
## [19658,] -122.4179 37.78362
## [19659,] -122.4084 37.74184
## [19660,] -122.4772 37.74443
## [19661,] -122.4008 37.71949
## [19662,] -122.3956 37.77723
## [19663,] -122.4313 37.74016
## [19664,] -122.4328 37.78732
## [19665,] -122.4793 37.77505
## [19666,] -122.4385 37.73102
## [19667,] -122.4295 37.75695
## [19668,] -122.4622 37.74530
## [19669,] -122.4891 37.76279
## [19670,] -122.4569 37.71347
## [19671,] -122.4647 37.71372
## [19672,] -122.4448 37.74481
## [19673,] -122.4551 37.76543
## [19674,] -122.3933 37.77891
## [19675,] -122.4412 37.80361
## [19676,] -122.5052 37.76088
## [19677,] -122.4015 37.79680
## [19678,] -122.4955 37.77231
## [19679,] -122.4011 37.77047
## [19680,] -122.4622 37.75742
## [19681,] -122.3960 37.72062
## [19682,] -122.4854 37.75537
## [19683,] -122.4889 37.75272
## [19684,] -122.5103 37.77376
## [19685,] -122.5064 37.77368
## [19686,] -122.4293 37.76231
## [19687,] -122.4647 37.75134
## [19688,] -122.4033 37.72220
## [19689,] -122.4344 37.76604
## [19690,] -122.4258 37.72119
## [19691,] -122.3904 37.73421
## [19692,] -122.4446 37.71320
## [19693,] -122.4822 37.76175
## [19694,] -122.4498 37.73357
## [19695,] -122.4154 37.79358
## [19696,] -122.4961 37.77806
## [19697,] -122.4010 37.71226
## [19698,] -122.4196 37.79002
## [19699,] -122.3937 37.78702
## [19700,] -122.4262 37.73586
## [19701,] -122.4886 37.73100
## [19702,] -122.4685 37.71946
## [19703,] -122.3958 37.77339
## [19704,] -122.5059 37.76251
## [19705,] -122.3984 37.72227
## [19706,] -122.4655 37.75645
## [19707,] -122.4780 37.76498
## [19708,] -122.5063 37.74593
## [19709,] -122.5023 37.74417
## [19710,] -122.4597 37.78226
## [19711,] -122.3930 37.75336
## [19712,] -122.4396 37.72328
## [19713,] -122.4443 37.80482
## [19714,] -122.4301 37.73506
## [19715,] -122.4188 37.77159
## [19716,] -122.4121 37.79689
## [19717,] -122.5039 37.74223
## [19718,] -122.4194 37.75596
## [19719,] -122.3978 37.77777
## [19720,] -122.4814 37.75901
## [19721,] -122.4305 37.76886
## [19722,] -122.3958 37.77339
## [19723,] -122.4143 37.74754
## [19724,] -122.4086 37.80108
## [19725,] -122.4810 37.76222
## [19726,] -122.4395 37.72392
## [19727,] -122.4423 37.73129
## [19728,] -122.4270 37.76711
## [19729,] -122.4815 37.78242
## [19730,] -122.4866 37.75054
## [19731,] -122.4403 37.80325
## [19732,] -122.4315 37.76005
## [19733,] -122.4794 37.77547
## [19734,] -122.4032 37.77837
## [19735,] -122.4584 37.75436
## [19736,] -122.4952 37.76446
## [19737,] -122.4836 37.74347
## [19738,] -122.4453 37.76295
## [19739,] -122.4672 37.72314
## [19740,] -122.4089 37.73247
## [19741,] -122.4313 37.77026
## [19742,] -122.4092 37.74269
## [19743,] -122.4124 37.80434
## [19744,] -122.4996 37.75868
## [19745,] -122.4551 37.78426
## [19746,] -122.4897 37.75157
## [19747,] -122.3922 37.78607
## [19748,] -122.4331 37.78659
## [19749,] -122.4529 37.71620
## [19750,] -122.4991 37.76024
## [19751,] -122.4415 37.74682
## [19752,] -122.4225 37.75661
## [19753,] -122.4377 37.73295
## [19754,] -122.4260 37.72088
## [19755,] -122.4158 37.78979
## [19756,] -122.3768 37.73227
## [19757,] -122.4267 37.74957
## [19758,] -122.3902 37.71084
## [19759,] -122.4418 37.80161
## [19760,] -122.3991 37.78165
## [19761,] -122.4605 37.75363
## [19762,] -122.5015 37.76263
## [19763,] -122.4324 37.76051
## [19764,] -122.4880 37.74583
## [19765,] -122.4194 37.75596
## [19766,] -122.4444 37.71703
## [19767,] -122.4223 37.79267
## [19768,] -122.4939 37.76182
## [19769,] -122.4389 37.77274
## [19770,] -122.4512 37.73511
## [19771,] -122.4649 37.78549
## [19772,] -122.4420 37.75106
## [19773,] -122.3910 37.78938
## [19774,] -122.3937 37.78702
## [19775,] -122.4410 37.80056
## [19776,] -122.4288 37.77116
## [19777,] -122.4497 37.76847
## [19778,] -122.4133 37.78070
## [19779,] -122.4091 37.75615
## [19780,] -122.4330 37.75562
## [19781,] -122.4654 37.78608
## [19782,] -122.3911 37.73912
## [19783,] -122.4449 37.78816
## [19784,] -122.4235 37.80312
## [19785,] -122.3910 37.78938
## [19786,] -122.4468 37.71655
## [19787,] -122.3991 37.78660
## [19788,] -122.4784 37.73093
## [19789,] -122.5076 37.77640
## [19790,] -122.4239 37.72899
## [19791,] -122.5069 37.77832
## [19792,] -122.4268 37.72841
## [19793,] -122.4694 37.72810
## [19794,] -122.4834 37.74160
## [19795,] -122.3991 37.73239
## [19796,] -122.4736 37.72656
## [19797,] -122.4566 37.71803
## [19798,] -122.4139 37.79575
## [19799,] -122.4240 37.78482
## [19800,] -122.4390 37.80069
## [19801,] -122.4429 37.71981
## [19802,] -122.4152 37.79845
## [19803,] -122.4294 37.74696
## [19804,] -122.4421 37.75062
## [19805,] -122.4469 37.76075
## [19806,] -122.4089 37.77291
## [19807,] -122.3978 37.72703
## [19808,] -122.5021 37.76289
## [19809,] -122.4261 37.76582
## [19810,] -122.4129 37.79564
## [19811,] -122.3951 37.72508
## [19812,] -122.4667 37.71133
## [19813,] -122.4110 37.73932
## [19814,] -122.4828 37.74218
## [19815,] -122.4825 37.73225
## [19816,] -122.4158 37.76224
## [19817,] -122.4788 37.74575
## [19818,] -122.4989 37.77834
## [19819,] -122.4553 37.71773
## [19820,] -122.4651 37.73860
## [19821,] -122.4136 37.74467
## [19822,] -122.4425 37.75060
## [19823,] -122.4507 37.78141
## [19824,] -122.3941 37.73004
## [19825,] -122.4392 37.75732
## [19826,] -122.3875 37.77166
## [19827,] -122.4144 37.71470
## [19828,] -122.3989 37.76054
## [19829,] -122.4970 37.73553
## [19830,] -122.4307 37.78619
## [19831,] -122.3922 37.78607
## [19832,] -122.4798 37.78437
## [19833,] -122.4312 37.79432
## [19834,] -122.4410 37.79189
## [19835,] -122.4486 37.73860
## [19836,] -122.3875 37.77166
## [19837,] -122.4097 37.77613
## [19838,] -122.4301 37.74120
## [19839,] -122.4474 37.71848
## [19840,] -122.4923 37.75940
## [19841,] -122.4473 37.77805
## [19842,] -122.4676 37.71048
## [19843,] -122.4281 37.78837
## [19844,] -122.4146 37.75379
## [19845,] -122.4435 37.75964
## [19846,] -122.4948 37.72995
## [19847,] -122.4299 37.73268
## [19848,] -122.4320 37.79973
## [19849,] -122.4376 37.75622
## [19850,] -122.5031 37.74080
## [19851,] -122.4485 37.77783
## [19852,] -122.4017 37.72748
## [19853,] -122.3702 37.72671
## [19854,] -122.4355 37.79843
## [19855,] -122.3987 37.75115
## [19856,] -122.3978 37.76053
## [19857,] -122.4291 37.75396
## [19858,] -122.3924 37.78355
## [19859,] -122.4287 37.79001
## [19860,] -122.4432 37.71298
## [19861,] -122.4364 37.73602
## [19862,] -122.4656 37.72001
## [19863,] -122.4616 37.72557
## [19864,] -122.4583 37.77774
## [19865,] -122.4608 37.72161
## [19866,] -122.4041 37.80347
## [19867,] -122.4661 37.74202
## [19868,] -122.4054 37.77809
## [19869,] -122.4156 37.72683
## [19870,] -122.4055 37.78164
## [19871,] -122.4690 37.74490
## [19872,] -122.4165 37.77528
## [19873,] -122.4332 37.76122
## [19874,] -122.4127 37.78995
## [19875,] -122.4527 37.78809
## [19876,] -122.4400 37.75069
## [19877,] -122.4172 37.75441
## [19878,] -122.3891 37.78624
## [19879,] -122.3867 37.73944
## [19880,] -122.4243 37.79352
## [19881,] -122.3997 37.76046
## [19882,] -122.4166 37.75247
## [19883,] -122.4564 37.71786
## [19884,] -122.4963 37.73563
## [19885,] -122.4630 37.77526
## [19886,] -122.4447 37.80385
## [19887,] -122.4996 37.73514
## [19888,] -122.4685 37.78419
## [19889,] -122.5076 37.74847
## [19890,] -122.4410 37.72471
## [19891,] -122.4134 37.72836
## [19892,] -122.5029 37.75911
## [19893,] -122.4871 37.76287
## [19894,] -122.4158 37.73404
## [19895,] -122.4238 37.74412
## [19896,] -122.3918 37.77863
## [19897,] -122.3934 37.77764
## [19898,] -122.5000 37.77262
## [19899,] -122.3871 37.73120
## [19900,] -122.4853 37.78038
## [19901,] -122.4160 37.72769
## [19902,] -122.3918 37.77899
## [19903,] -122.4952 37.73633
## [19904,] -122.4230 37.79056
## [19905,] -122.4660 37.74957
## [19906,] -122.4396 37.78078
## [19907,] -122.5037 37.75092
## [19908,] -122.4356 37.75859
## [19909,] -122.4292 37.72741
## [19910,] -122.5066 37.74568
## [19911,] -122.4335 37.71398
## [19912,] -122.5064 37.77873
## [19913,] -122.4726 37.75051
## [19914,] -122.4032 37.78824
## [19915,] -122.4276 37.80130
## [19916,] -122.4243 37.73766
## [19917,] -122.3852 37.72630
## [19918,] -122.4700 37.75086
## [19919,] -122.4339 37.73009
## [19920,] -122.4037 37.76450
## [19921,] -122.4286 37.79534
## [19922,] -122.4302 37.76078
## [19923,] -122.4323 37.79641
## [19924,] -122.4656 37.72110
## [19925,] -122.4326 37.79789
## [19926,] -122.4983 37.76360
## [19927,] -122.4034 37.71991
## [19928,] -122.4056 37.78065
## [19929,] -122.4207 37.72958
## [19930,] -122.3942 37.77181
## [19931,] -122.4317 37.73270
## [19932,] -122.4590 37.71972
## [19933,] -122.4261 37.73585
## [19934,] -122.4339 37.76607
## [19935,] -122.3934 37.77764
## [19936,] -122.4214 37.74370
## [19937,] -122.4943 37.75296
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## [19939,] -122.4519 37.76488
## [19940,] -122.4422 37.73360
## [19941,] -122.4878 37.73287
## [19942,] -122.4149 37.79362
## [19943,] -122.4304 37.73897
## [19944,] -122.4214 37.79256
## [19945,] -122.4406 37.75725
## [19946,] -122.4610 37.72833
## [19947,] -122.4319 37.72930
## [19948,] -122.4953 37.74377
## [19949,] -122.4460 37.74805
## [19950,] -122.4543 37.78055
## [19951,] -122.4332 37.78782
## [19952,] -122.4019 37.71512
## [19953,] -122.4334 37.75901
## [19954,] -122.4934 37.76073
## [19955,] -122.4125 37.77600
## [19956,] -122.4031 37.79058
## [19957,] -122.4666 37.78637
## [19958,] -122.4265 37.74463
## [19959,] -122.4381 37.78210
## [19960,] -122.5044 37.75925
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## [19962,] -122.4176 37.75779
## [19963,] -122.4202 37.73972
## [19964,] -122.4712 37.77707
## [19965,] -122.4493 37.71446
## [19966,] -122.4097 37.71962
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## [19976,] -122.4372 37.77728
## [19977,] -122.4012 37.79226
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## [19985,] -122.4878 37.75243
## [19986,] -122.4423 37.71685
## [19987,] -122.4317 37.77703
## [19988,] -122.4501 37.73752
## [19989,] -122.4176 37.74217
## [19990,] -122.4586 37.76598
## [19991,] -122.4242 37.79788
## [19992,] -122.4151 37.78524
## [19993,] -122.4291 37.73972
## [19994,] -122.4199 37.78999
## [19995,] -122.4420 37.78570
## [19996,] -122.4050 37.80264
## [19997,] -122.4403 37.71691
## [19998,] -122.3944 37.75357
## [19999,] -122.4082 37.72882
## [20000,] -122.4101 37.77921
## [20001,] -122.4422 37.72554
## [20002,] -122.4705 37.71847
## [20003,] -122.4308 37.71198
## [20004,] -122.4734 37.74627
## [20005,] -122.3940 37.76377
## [20006,] -122.4188 37.77159
## [20007,] -122.4620 37.71719
## [20008,] -122.3998 37.72926
## [20009,] -122.4528 37.71555
## [20010,] -122.3969 37.78471
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## [20012,] -122.4379 37.78241
## [20013,] -122.4155 37.71143
## [20014,] -122.4746 37.76235
## [20015,] -122.4303 37.74855
## [20016,] -122.4372 37.74845
## [20017,] -122.5070 37.75691
## [20018,] -122.4706 37.71089
## [20019,] -122.4360 37.79818
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## [20021,] -122.5086 37.77921
## [20022,] -122.4693 37.75260
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## [20024,] -122.3932 37.78006
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## [20029,] -122.4369 37.76096
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## [20035,] -122.4441 37.76801
## [20036,] -122.4251 37.79124
## [20037,] -122.4142 37.77031
## [20038,] -122.3930 37.75336
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## [20040,] -122.3922 37.72964
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## [20044,] -122.4579 37.72931
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## [20048,] -122.3708 37.72707
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## [20051,] -122.4569 37.74423
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## [24800,] -122.4187 37.74791
## [24801,] -122.4426 37.75614
## [24802,] -122.4292 37.79769
## [24803,] -122.4418 37.70831
## [24804,] -122.4511 37.70849
## [24805,] -122.3907 37.78360
## [24806,] -122.4344 37.75882
## [24807,] -122.3933 37.71205
## [24808,] -122.4127 37.78628
## [24809,] -122.4564 37.78261
## [24810,] -122.4380 37.73731
## [24811,] -122.3937 37.78702
## [24812,] -122.4075 37.70846
## [24813,] -122.4280 37.79680
## [24814,] -122.4022 37.72486
## [24815,] -122.4536 37.78076
## [24816,] -122.4009 37.72799
## [24817,] -122.4048 37.79879
## [24818,] -122.4189 37.74283
## [24819,] -122.3853 37.72954
## [24820,] -122.3947 37.77419
## [24821,] -122.4031 37.79058
## [24822,] -122.4188 37.76370
## [24823,] -122.4374 37.72798
## [24824,] -122.4270 37.76378
## [24825,] -122.4194 37.79362
## [24826,] -122.4270 37.72591
## [24827,] -122.4096 37.75985
## [24828,] -122.4312 37.78759
## [24829,] -122.4991 37.77468
## [24830,] -122.4348 37.74747
## [24831,] -122.4938 37.74441
## [24832,] -122.4133 37.78930
## [24833,] -122.4342 37.76055
## [24834,] -122.4370 37.79767
## [24835,] -122.5070 37.75005
## [24836,] -122.4267 37.73761
## [24837,] -122.5051 37.75279
## [24838,] -122.4245 37.77784
## [24839,] -122.4154 37.73813
## [24840,] -122.4704 37.74936
## [24841,] -122.4911 37.73560
## [24842,] -122.4364 37.78702
## [24843,] -122.4219 37.77255
## [24844,] -122.4264 37.77024
## [24845,] -122.4364 37.75549
## [24846,] -122.4839 37.74185
## [24847,] -122.4785 37.77682
## [24848,] -122.4376 37.71420
## [24849,] -122.4673 37.75229
## [24850,] -122.3986 37.72789
## [24851,] -122.4235 37.78038
## [24852,] -122.4439 37.79010
## [24853,] -122.4207 37.76911
## [24854,] -122.4675 37.73654
## [24855,] -122.4207 37.80509
## [24856,] -122.4552 37.71689
## [24857,] -122.4139 37.77622
## [24858,] -122.4397 37.71435
## [24859,] -122.4041 37.80347
## [24860,] -122.4293 37.71854
## [24861,] -122.3907 37.78360
## [24862,] -122.4043 37.78622
## [24863,] -122.4741 37.73601
## [24864,] -122.4539 37.78453
## [24865,] -122.4076 37.77724
## [24866,] -122.4287 37.75700
## [24867,] -122.4608 37.78235
## [24868,] -122.4040 37.78923
## [24869,] -122.4702 37.76304
## [24870,] -122.4116 37.79284
## [24871,] -122.3959 37.79054
## [24872,] -122.4236 37.77800
## [24873,] -122.4023 37.72099
## [24874,] -122.4964 37.75821
## [24875,] -122.4759 37.75191
## [24876,] -122.4321 37.72976
## [24877,] -122.4719 37.72139
## [24878,] -122.4897 37.77808
## [24879,] -122.4122 37.79293
## [24880,] -122.4259 37.76544
## [24881,] -122.4300 37.78810
## [24882,] -122.4248 37.80543
## [24883,] -122.4003 37.73079
## [24884,] -122.4780 37.78122
## [24885,] -122.3970 37.76017
## [24886,] -122.4015 37.77332
## [24887,] -122.4163 37.72453
## [24888,] -122.4208 37.74527
## [24889,] -122.4229 37.80586
## [24890,] -122.4893 37.77249
## [24891,] -122.4474 37.73183
## [24892,] -122.4163 37.77209
## [24893,] -122.4027 37.71927
## [24894,] -122.3910 37.78938
## [24895,] -122.4326 37.71534
## [24896,] -122.4441 37.73437
## [24897,] -122.4192 37.75126
## [24898,] -122.4339 37.72900
## [24899,] -122.4243 37.79352
## [24900,] -122.3904 37.78139
## [24901,] -122.4300 37.74857
## [24902,] -122.4081 37.78469
## [24903,] -122.4233 37.72451
## [24904,] -122.4214 37.78139
## [24905,] -122.4074 37.71731
## [24906,] -122.4866 37.73322
## [24907,] -122.4913 37.74694
## [24908,] -122.4127 37.78995
## [24909,] -122.4443 37.71540
## [24910,] -122.4265 37.75070
## [24911,] -122.4392 37.71404
## [24912,] -122.4928 37.73705
## [24913,] -122.4175 37.74033
## [24914,] -122.4729 37.73576
## [24915,] -122.4375 37.77913
## [24916,] -122.4591 37.77905
## [24917,] -122.4179 37.72410
## [24918,] -122.4286 37.76027
## [24919,] -122.5075 37.74749
## [24920,] -122.3909 37.75967
## [24921,] -122.4137 37.79099
## [24922,] -122.4446 37.77193
## [24923,] -122.4910 37.75797
## [24924,] -122.4261 37.79383
## [24925,] -122.5036 37.74591
## [24926,] -122.4305 37.76416
## [24927,] -122.4761 37.78220
## [24928,] -122.4817 37.73357
## [24929,] -122.4303 37.72021
## [24930,] -122.4954 37.77558
## [24931,] -122.4263 37.76886
## [24932,] -122.4166 37.74088
## [24933,] -122.4229 37.73206
## [24934,] -122.3937 37.78702
## [24935,] -122.4128 37.77594
## [24936,] -122.4949 37.73496
## [24937,] -122.4764 37.74817
## [24938,] -122.4857 37.78247
## [24939,] -122.4938 37.76013
## [24940,] -122.4192 37.72509
## [24941,] -122.4188 37.77159
## [24942,] -122.4371 37.74524
## [24943,] -122.4355 37.73419
## [24944,] -122.4501 37.75411
## [24945,] -122.4316 37.75571
## [24946,] -122.4192 37.75730
## [24947,] -122.4607 37.78607
## [24948,] -122.4853 37.75335
## [24949,] -122.4356 37.72596
## [24950,] -122.4351 37.73582
## [24951,] -122.4067 37.80057
## [24952,] -122.4699 37.78028
## [24953,] -122.5054 37.76376
## [24954,] -122.4742 37.78088
## [24955,] -122.4104 37.71113
## [24956,] -122.4731 37.76162
## [24957,] -122.4249 37.76280
## [24958,] -122.4761 37.74511
## [24959,] -122.3819 37.72541
## [24960,] -122.4458 37.76752
## [24961,] -122.4089 37.78377
## [24962,] -122.4153 37.77445
## [24963,] -122.4814 37.73374
## [24964,] -122.4481 37.77403
## [24965,] -122.4601 37.77852
## [24966,] -122.3919 37.78868
## [24967,] -122.4948 37.77932
## [24968,] -122.4320 37.78645
## [24969,] -122.4725 37.76515
## [24970,] -122.4347 37.74860
## [24971,] -122.4249 37.76548
## [24972,] -122.4382 37.73261
## [24973,] -122.4185 37.80365
## [24974,] -122.4809 37.75186
## [24975,] -122.4159 37.73586
## [24976,] -122.4101 37.78945
## [24977,] -122.4436 37.72009
## [24978,] -122.3910 37.78938
## [24979,] -122.4207 37.78509
## [24980,] -122.4646 37.75156
## [24981,] -122.3886 37.77159
## [24982,] -122.3967 37.73172
## [24983,] -122.4458 37.73512
## [24984,] -122.4188 37.77159
## [24985,] -122.4335 37.77218
## [24986,] -122.4668 37.77558
## [24987,] -122.4580 37.71255
## [24988,] -122.4481 37.78154
## [24989,] -122.4429 37.75567
## [24990,] -122.4479 37.77947
## [24991,] -122.4281 37.73668
## [24992,] -122.3986 37.76049
## [24993,] -122.5087 37.77462
## [24994,] -122.4420 37.74622
## [24995,] -122.4362 37.71472
## [24996,] -122.4279 37.75142
## [24997,] -122.4948 37.73555
## [24998,] -122.3848 37.72735
## [24999,] -122.4062 37.77270
## [25000,] -122.4633 37.72539

str(sfhomes15) # the data frame

str(sfhomes15_sp) # the data frame

str(sfhomes15) # the data frame

## 'data.frame':    835 obs. of  19 variables:
##  $ FiscalYear      : int  2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 ...
##  $ SalesDate       : chr  "2015-08-21" "2015-08-13" "2015-12-29" "2015-08-26" ...
##  $ Address         : chr  "0000 2760 19TH                AV0015" "0000 0560AMISSOURI            ST0000" "0000 0718 LONG BRIDGE         ST1202" "0000 0103 SUMMIT              WY0000" ...
##  $ YearBuilt       : int  1979 2003 2016 NA 2015 1961 1973 1900 NA 2015 ...
##  $ NumBedrooms     : int  2 2 2 3 3 3 3 2 0 2 ...
##  $ NumBathrooms    : int  2 2 2 3 3 3 3 2 0 2 ...
##  $ NumRooms        : int  5 5 5 6 7 7 7 5 0 0 ...
##  $ NumStories      : int  0 1 1 0 1 14 2 1 0 1 ...
##  $ NumUnits        : int  1 1 1 1 1 1 1 1 0 1 ...
##  $ AreaSquareFeet  : int  1595 1191 1346 2133 1266 1840 2075 1256 0 1520 ...
##  $ ImprovementValue: int  432500 701280 1512093 582108 850000 1154846 484544 810169 486872 962500 ...
##  $ LandValue       : int  432500 701280 748900 873161 850000 1154846 1130604 1890395 1136036 962500 ...
##  $ Neighborhood    : chr  "West of Twin Peaks" "Potrero Hill" "Mission Bay" "Lakeshore" ...
##  $ Location        : chr  "(37.7360097396496, -122.474067310226)" "(37.759197817252, -122.396516184449)" "(37.7718055392903, -122.394186974738)" "(37.7151803909173, -122.475425717555)" ...
##  $ SupeDistrict    : int  7 10 6 7 9 3 8 2 7 6 ...
##  $ totvalue        : int  865000 1402560 2260993 1455269 1700000 2309692 1615148 2700564 1622908 1925000 ...
##  $ SalesYear       : int  2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 ...
##  $ lat             : num  37.7 37.8 37.8 37.7 37.8 ...
##  $ lon             : num  -122 -122 -122 -122 -122 ...

str(sfhomes15_sp) # the SPDF

## Formal class 'SpatialPointsDataFrame' [package "sp"] with 5 slots
##   ..@ data       :'data.frame':  25000 obs. of  17 variables:
##   .. ..$ FiscalYear      : int [1:25000] 2015 2015 2015 2015 2015 2015 2015 2015 2015 2015 ...
##   .. ..$ SalesDate       : chr [1:25000] "2010-09-14" NA "2014-09-18" NA ...
##   .. ..$ Address         : chr [1:25000] "0000 0136 CORONA              ST0000" "0000 0197 PARKER              AV0000" "0000 0755 09TH                AV0000" "0000 1939 44TH                AV0000" ...
##   .. ..$ YearBuilt       : int [1:25000] 1923 1909 1915 1947 1981 1916 1923 2003 1925 1890 ...
##   .. ..$ NumBedrooms     : int [1:25000] 0 3 2 0 3 5 4 3 4 6 ...
##   .. ..$ NumBathrooms    : int [1:25000] 0 3 2 0 3 5 4 3 4 6 ...
##   .. ..$ NumRooms        : int [1:25000] 7 10 6 5 6 9 8 7 10 11 ...
##   .. ..$ NumStories      : int [1:25000] 1 2 1 1 2 2 2 4 2 3 ...
##   .. ..$ NumUnits        : int [1:25000] 1 1 1 1 1 1 1 1 1 1 ...
##   .. ..$ AreaSquareFeet  : int [1:25000] 2250 5830 1350 1162 1463 2304 4440 1860 3330 2246 ...
##   .. ..$ ImprovementValue: int [1:25000] 412556 360604 558386 344050 133307 328453 665081 314062 107655 116024 ...
##   .. ..$ LandValue       : int [1:25000] 618835 414696 558386 516080 189442 766392 297525 314062 41295 71386 ...
##   .. ..$ Neighborhood    : chr [1:25000] "West of Twin Peaks" "Presidio Heights" "Inner Richmond" "Sunset/Parkside" ...
##   .. ..$ Location        : chr [1:25000] "(37.7241608039084, -122.466027966231)" "(37.7818771834593, -122.454422773958)" "(37.7741726275595, -122.46733933124)" "(37.7504189882518, -122.503409333331)" ...
##   .. ..$ SupeDistrict    : int [1:25000] 7 2 1 4 1 4 7 10 1 9 ...
##   .. ..$ totvalue        : int [1:25000] 1031391 775300 1116772 860130 322749 1094845 962606 628124 148950 187410 ...
##   .. ..$ SalesYear       : int [1:25000] 2010 NA 2014 NA 1995 2012 NA 1950 NA NA ...
##   ..@ coords.nrs : int [1:2] 19 18
##   ..@ coords     : num [1:25000, 1:2] -122 -122 -122 -123 -122 ...
##   .. ..- attr(*, "dimnames")=List of 2
##   .. .. ..$ : NULL
##   .. .. ..$ : chr [1:2] "lon" "lat"
##   ..@ bbox       : num [1:2, 1:2] -122.5 37.7 -122.4 37.8
##   .. ..- attr(*, "dimnames")=List of 2
##   .. .. ..$ : chr [1:2] "lon" "lat"
##   .. .. ..$ : chr [1:2] "min" "max"
##   ..@ proj4string:Formal class 'CRS' [package "sp"] with 1 slot
##   .. .. ..@ projargs: chr NA

You can see from str(sfhomes) that a SPDF object is a collection of slots or components. The key ones are:

• @data data frame of attributes that describe each location
• @coords the coordinates for each geometric object - here points
• @bbox the min and max bounding coordinates
• @proj4string the coordinate reference system defintion as a string

Explore the object in the Environment window

Review the output of each of these:

summary(sfhomes15_sp)
head(sfhomes15_sp@data)
class(sfhomes15_sp@data)

sfhomes15_sp@bbox
bbox(sfhomes15_sp)

head(sfhomes15_sp@coords)
head(sfhomes15_sp$lat)
head(sfhomes15_sp$lon)

sfhomes15_sp@proj4string
proj4string(sfhomes15_sp)

Look at sfhomes15_sp in the environment window

Are all the columns that were present in sfhomes15 also in sfhomes15_sp?

Is there a slot in sfhomes15_sp without data?

proj4string(sfhomes15_sp) # get a CRS object

## [1] NA

plot(sfhomes15_sp)  # using sp::plot

We created great maps of sfhomes point data with ggplot and ggmap.

Then we created a simple map of the SPDF with plot.

We aren’t seeing the value of sp objects just yet.

rgdal is an R port of the powerful and widely used GDAL library.

It is the most commonly used R library for importing and exporting spatial data.

• OGR: for vector data: readOGR() and writeOGR()

• GDAL for raster data: readGDAL() and writeGDAL()

library(rgdal)

## rgdal: version: 1.3-6, (SVN revision 773)
##  Geospatial Data Abstraction Library extensions to R successfully loaded
##  Loaded GDAL runtime: GDAL 2.3.2, released 2018/09/21
##  Path to GDAL shared files: /usr/share/gdal
##  GDAL binary built with GEOS: TRUE 
##  Loaded PROJ.4 runtime: Rel. 5.2.0, September 15th, 2018, [PJ_VERSION: 520]
##  Path to PROJ.4 shared files: (autodetected)
##  Linking to sp version: 1.3-1

# See what file types are supported by rgdal drivers
# ogrDrivers()$name

gdal.org

?readOGR

For more info on working with rgdal to load different types of spatial data in R see this excellent tutorial by Zev Ross.

Take a look at the file(s)

dir("data", pattern="sf_boundary")

##  [1] "sf_boundary_geo.dbf"  "sf_boundary_geo.prj"  "sf_boundary_geo.shp" 
##  [4] "sf_boundary_geo.shx"  "sf_boundary_geo2.dbf" "sf_boundary_geo2.prj"
##  [7] "sf_boundary_geo2.shp" "sf_boundary_geo2.shx" "sf_boundary.dbf"     
## [10] "sf_boundary.prj"      "sf_boundary.shp"      "sf_boundary.shx"

sfboundary <- readOGR(dsn="data",layer="sf_boundary")

## OGR data source with driver: ESRI Shapefile 
## Source: "/home/drew/Desktop/stuff/berk/dlab/r-geospatial-workshop/data", layer: "sf_boundary"
## with 1 features
## It has 3 fields

# or
# sfboundary <- readOGR("data","sf_boundary")
# but not
#sfboundary <- readOGR(dsn="data/",layer="sf_boundary")

What type of sp object is sfboundary? How many features are in the object?

class(sfboundary)
str(sfboundary) 
head(sfboundary@data)  

Explore the object in the Envi window

How?

plot(sfboundary)

plot(sfboundary)
points(sfhomes15_sp, col="red")

Where are the points? What’s wrong?

plot(sfboundary)
points(sfhomes15_sp, col="red")

Compare the CRSs, are they the same?

proj4string(sfboundary)
proj4string(sfhomes15_sp)

proj4string(sfboundary)

## [1] "+proj=utm +zone=10 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs"

proj4string(sfhomes15_sp)

## [1] NA

sfboundary@bbox

##         min       max
## x  542696.6  556659.9
## y 4173563.7 4185088.6

sfhomes15_sp@bbox

##            min        max
## lon -122.51091 -122.36747
## lat   37.70817   37.80801

The #1 reason…

All sp objects should have a defined CRS

If not, one needs to be assigned to the object

• This is called defining a projection

• This doesn’t change the coordinates

All sp objects should have the same CRS.

This CRS should be defined in the proj4string slot.

• When they don’t, they need to be transformed to a common CRS.

• This is called a projection transformation,
  • or projecting or reprojection.

Projection transformation returns a new spatial object with the transformed coordinates

GIS software - or software for working with geospatial data - will have a database of definitions for thousands of Earth referenced coordinate systems

and methods for using those CRS definitions to define or transform a CRS.

So, do we need to define the CRS of either

• sfboundary or

• sfhomes15_sp?

If yes, which one? How can you tell?

We need to know

• what the data’s CRS is
• how to define it for the sp object

bbox(sfhomes15_sp)

##            min        max
## lon -122.51091 -122.36747
## lat   37.70817   37.80801

Use the sp function CRS() to create a CRS object

Then, use the sp::proj4string() to assign it

# Define the CRS for sfhomes15_sp as WGS84

proj4string(sfhomes15_sp) <- CRS("+proj=longlat 
                               +ellps=WGS84 +datum=WGS84 +no_defs")  

The WGS84 proj4 string

CRS("+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs")

The WGS84 epsg code

CRS("+init=epsg:4326")

EPSG refers to the group that defined these

• European Petroleum Survey Group

EPSG codes are more commonly used. Can you guess why?

# use an EPSG code for WGS84
proj4string(sfhomes15_sp) <- CRS("+init=epsg:4326") 

# or enter the parameter string
# proj4string(sfhomes15_sp) <- CRS("+proj=longlat 
#                               +ellps=WGS84 +datum=WGS84 +no_defs")  

Proj4 is the standard library for defining and transforming map projections and coordinate reference systems.

Here is an example file of proj4 CRS definitions

Once you set the CRS you can check it with the same function.

proj4string(sfhomes15_sp)

## [1] "+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs +towgs84=0,0,0"

proj4string() can get or set the CRS

CRS() is used to define the CRS of an sp object

The following are equivalent

# Define the CRS with the parameter string
proj4string(sfhomes15_sp) <- CRS("+proj=longlat 
                              +ellps=WGS84 +datum=WGS84 +no_defs")  

# Define the CRS with an EPSG code for WGS84
proj4string(sfhomes15_sp) <- CRS("+init=epsg:4326") 

epsg codes are used as short-hand for CRSs definitions

Are they both defined? Are they the same?

proj4string(sfboundary)

## [1] "+proj=utm +zone=10 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs"

proj4string(sfhomes15_sp)

## [1] "+proj=longlat +ellps=WGS84 +datum=WGS84 +no_defs +towgs84=0,0,0"

proj4string(sfboundary) == proj4string(sfhomes15_sp)

## [1] FALSE

Use sp function spTransform

Requires as input:

• a sp object to transform with a defined CRS

• a target CRS

Outputs a new spatial object with coordinate data in the target CRS

• It does not change the input data

Let’s transform the CRS of sfboundary to be the same as that of sfhomes15_sp.

sfboundary_lonlat <- spTransform(sfboundary, CRS("+init=epsg:4326"))

Why not the other way around?

Do they match now?

How will we know?

proj4string(sfhomes15_sp) == proj4string(sfboundary_lonlat)

## [1] FALSE

plot(sfboundary_lonlat)
points(sfhomes15_sp, col="red")

Woo-hoo!

We can define the CRS of sp objects and transform them to the same CRS for mapping and spatial analysis.

Recap

# Define the CRS
proj4string(sfhomes15_sp) <- CRS("+init=epsg:4326")

#Transform the CRS
sfboundary_lonlat <- spTransform(sfboundary, CRS("+init=epsg:4326"))

Use writeOGR to save sfboundary_lonlat to a new shapefile

See ?writeOGR for help

# write transformed data to a new shapefile 
writeOGR(sfboundary_lonlat, 
          dsn = "data", 
          layer = "sfbounary_lonlat", 
          driver="ESRI Shapefile")

# is it there?
dir("data")

=

We want all data in the same CRS

Which one is best?

Geographic CRSs

• 4326 Geographic, WGS84 (default for lon/lat)

• 4269 Geographic, NAD83 (USA Fed agencies like Census)

Projected CRSs

• 5070 USA Contiguous Albers Equal Area Conic

• 3310 CA ALbers Equal Area

• 26910 UTM Zone 10, NAD83 (Northern Cal)

• 3857 Web Mercator (web maps)

See http://spatialreference.org/

Use this site to find EPSG codes and proj4 CRS strings

1. Use coordinates to convert the landmarks data frame to a SpatialPointsDataFrame
2. Use proj4string to define it’s CRS as 3857 Web Mercator
3. Use spTransform to transform the landmarks data to geographic coords (WGS84)
4. Add the landmarks to the last map we created.

# Convert the DF to a SPDF
coordinates(landmarks) <-c("X","Y")
# Define the CRS with an EPSG code for Web mercator
proj4string(landmarks) <- CRS("+init=epsg:3857") 
# Transform the CRS to WGS84
landmarks_lonlat <- spTransform(landmarks, CRS("+init=epsg:4326"))
# map it
plot(sfboundary_lonlat)
points(sfhomes15_sp, col="red")
points(landmarks_lonlat, col="green")

Note: Now that we’ve transformed our landmarks’ coordinates to geographic coordinates, let’s see how to get geocoded coordinates from gmap, to see how the results compare:

#prep our names for geocoding with the Google Maps API
place_names = paste0(landmarks@data$name, ',  San Francisco, CA')
#geocode them
geocode_coords = geocode(place_names)

## Source : https://maps.googleapis.com/maps/api/geocode/json?address=Coit+Tower,+San+Francisco,+CA&key=xxx

## "Coit Tower,  San ..." not uniquely geocoded, using "coit tower, san francisco, ca 94133, usa"

## Source : https://maps.googleapis.com/maps/api/geocode/json?address=Twin+Peaks,+San+Francisco,+CA&key=xxx

## Source : https://maps.googleapis.com/maps/api/geocode/json?address=City+Hall,+San+Francisco,+CA&key=xxx

## Source : https://maps.googleapis.com/maps/api/geocode/json?address=Golden+Gate+Park,+San+Francisco,+CA&key=xxx

#transformed coords
landmarks_lonlat@coords

##              X        Y
## [1,] -122.4058 37.80239
## [2,] -122.4476 37.75251
## [3,] -122.4193 37.77926
## [4,] -122.4862 37.76942

#geocoded coords
geocode_coords

## # A tibble: 4 x 2
##     lon   lat
##   <dbl> <dbl>
## 1 -122.  37.8
## 2 -122.  37.8
## 3 -122.  37.8
## 4 -122.  37.8

Nice! But why so little precision?

There are actually more significant digits. They’re just truncated by R’s display.

#transformed coords
landmarks_lonlat@coords

##              X        Y
## [1,] -122.4058 37.80239
## [2,] -122.4476 37.75251
## [3,] -122.4193 37.77926
## [4,] -122.4862 37.76942

#geocoded coords
cbind(geocode_coords$lon, geocode_coords$lat)

##           [,1]     [,2]
## [1,] -122.4058 37.80269
## [2,] -122.4476 37.75251
## [3,] -122.4193 37.77926
## [4,] -122.4862 37.76942

1. Use readOGR to load the shapefile “data/sf_highways.shp”
2. Check its data type with class()
3. Check its CRS with proj4string()
4. Use spTransform if need to project it to WGS84
5. Recreate the last map and add the highways as black lines

highways <- readOGR(dsn="data", layer="sf_highways")
class(highways)
proj4string(highways)
highways_lonlat <- spTransform(highways, CRS("+init=epsg:4326"))

plot(sfboundary_lonlat)
lines(highways_lonlat, col="black")
points(sfhomes15_sp, col="red")
points(landmarks_lonlat, col="green")

## OGR data source with driver: ESRI Shapefile 
## Source: "/home/drew/Desktop/stuff/berk/dlab/r-geospatial-workshop/data", layer: "sf_highways"
## with 246 features
## It has 5 fields

## [1] "SpatialLinesDataFrame"
## attr(,"package")
## [1] "sp"

## [1] "+proj=utm +zone=10 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs"

# QUESTIONS?

• Geospatial Data in R
• CSV > Data Frame > ggplot/ggmap
• sp library - spatial objects and methods in R
• GDAL libary - readOGR, writeOGR
• Convert Data Frame to SPDF
• CRS definitions and transformations
• Map Overlays